Question: Solve for $x$ and $y$ using elimination. ${-4x-2y = -42}$ ${-3x-2y = -36}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${4x+2y = 42}$ $-3x-2y = -36$ Add the top and bottom equations together. ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-4x-2y = -42}\thinspace$ to find $y$ ${-4}{(6)}{ - 2y = -42}$ $-24-2y = -42$ $-24{+24} - 2y = -42{+24}$ $-2y = -18$ $\dfrac{-2y}{{-2}} = \dfrac{-18}{{-2}}$ ${y = 9}$ You can also plug ${x = 6}$ into $\thinspace {-3x-2y = -36}\thinspace$ and get the same answer for $y$ : ${-3}{(6)}{ - 2y = -36}$ ${y = 9}$